Optimize inversion for O(n) time
Last updated: December 12, 2025
Quick Overview
Given an array of integers, your task is to count the number of inversions in the array in O(n) time. An inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. You should return the total count of such inversions as an integer.
TikTok
December 12, 20257
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4,794 solved
Given an array of integers, your task is to count the number of inversions in the array in O(n) time. An inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. You should return the total count of such inversions as an integer.
Coding interviews at TikTok focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- What if the input doesn't fit in memory?
- How would your solution change if the input was sorted?
- How would you modify your solution to handle streaming input?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Problem Analysis
To solve the problem of counting inversions in an array, we need to identify pairs of indices (i, j) where i < j and arr[i] > arr[j]. The challenge lies in achieving this in O(n) time. Typically, coun...
Approach
- Initialize a hash map to keep track of the frequency of each element in the array.
- Iterate through the array from right to left. For each element arr[i]:
- Before adding it to the hash map, c...
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